How do you find the derivative for $(-7x^2+8)^8(3x^2+9)^10$ ?

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Answer 1 · 2018-07-04T22:05:50

$\frac{dy}{dx}=-4x(189x^2+132)(-7x^2+8)^7(3x^2+9)^9$

Using product rule of differentiation as follows

$\frac{d}{dx}(-7x^2+8)^8(3x^2+9)^10$

$=(-7x^2+8)^8\frac{d}{dx}(3x^2+9)^10+(3x^2+9)^10\frac{d}{dx}(-7x^2+8)^8$

$=(-7x^2+8)^8(10(3x^2+9)^9)\frac{d}{dx}(3x^2+9)+(3x^2+9)^10(8(-7x^2+8)^7)\frac{d}{dx}(-7x^2+8)$

$=10(-7x^2+8)^8(3x^2+9)^9(6x)+8(3x^2+9)^10(-7x^2+8)^7(-14x)$

$=4x(-7x^2+8)^7(3x^2+9)^9(15(-7x^2+8)-28(3x^2+9))$

$=4x(-7x^2+8)^7(3x^2+9)^9(-189x^2-132)$

$=-4x(189x^2+132)(-7x^2+8)^7(3x^2+9)^9$

How do you find the derivative for (-7x^2+8)^8(3x^2+9)^10(-7x^2+8)^8(3x^2+9)^10?